Striker Josh Allen scored four times at Hartpury University in what was a rampant display from the young Hatters.
Allen started the scoring in the opening minute after Town made the perfect start, converting Jake Burger’s cross from close range.
Millar Matthews-Lewis doubled the Hatters’ advantage with his second goal in as many matches, calmly dispatching past the ‘keeper.
Forest Green pulled a goal back in the 35th minute but hopes of a comeback were dashed before half-time after Aidan Francis-Clarke and a second goal from Allen gave the Hatters a three-goal cushion at the break.
The striker secured his hat-trick five minutes after the restart following a lofted ball forward from Matthews-Lewis, before adding his fourth with arguably his best finish of the afternoon inside the area.
Substitute Archie Heron headed in a seventh in the latter stages, rounding off a brilliant 90 minutes for the Hatters which saw them comfortably through to the last four of the competition.
Town: Cowler; Swan (Heron 62), Francis-Clarke, Wedd, Johnson; Hemlin, Newton (Moffat 62), Matthews-Lewis (Odell-Bature 73), Burger; Lynch, Allen.
Goals: Allen (1’, 45’, 50’, 85’), Matthews-Lewis (12’), Francis-Clarke (42’), Heron (88’)